From the previous posting, you should have a feel for how Delta can help you gauge an option's likely movement for a one point movement in the underlying security. Delta is dynamic, so that, if the option becomes deeper and deeper in-the-money (ITM) the Delta will approach one, or if the option gets further and further out-of-the-money (OTM) Delta will approach zero.
This is only part one of a two-part story, though. Delta not only moves as the underlying security moves; it also moves as expiration approaches.
To better explain this concept I need to introduce to another definition of Delta, one used often by market markers: Delta is the probability of the option contract being in-the-money at expiration. You won't see this definition in text books. Rightly so, it is not the exact math formula used to calculate Delta. For learing about Delta it is good enough. I use this "non-standard" version to explain how and why Delta changes as expiration approaches.
Say we have an ATM call at 50 strike, the stock is at 50, and there's one day remaining to expiration. Delta in this case will be exactly 50. Why? If the stock goes up, the call will be in-the-money; if it goes down the option will be out-of-the-money. In other words, you have a 50/50 chance of the option finishing in-the-money on expiration; hence, Delta is 50.
Now consider a 50 strike call option that is already in-the-money with one day remaining; the stock is at 52. What's the Delta now? Think about the second definition. Being two points in-the-money with only one day remaining means the stock has a very high likelihood of staying in-the-money. That likelihood translates into a much larger Delta, close to 95.
If we lengthen the time to expiration in the last example, it vastly changes the way the option will act. Let's now say the option has 60 days remaining until expiration, the stock is still at 52 and the call strike is still 50. Now, what's the probability of the option being in-the-money at expiration? It's much lower because the stock has time to move. Delta on this option will be between 65 and 70. Here's another way to put it: more time to move means less likelihood of the option still being in-the-money at expiration; this translates into a smaller Delta.
Below is a table of actual Deltas from the marketplace. These Deltas are from options based on the S&P 500 Exchange Traded Fund (ETF), called the Spiders.
In this example, the April options had 11 days remaining until expiration and the July options had 158 days remaining. The 127 strike call has a much larger Delta, 80, compared to the July option, 65. With only 11 days remaining the April option had a much high likelihood of still being ITM at expiration, hence the higher Delta.
Now, let's talk about how the delta is affected by time on out-of-the-money options. Look at the 133 strikes in the chart; the July option's Delta is much higher than that of the April option. That's because, for a July option, time is now your friend: if you're buying OTM options, you need time for the stock to move up to the strike price. In other words, there's a much higher probability of the underlying finishing ITM for the July option than for the April; Delta reflects that probability.
The moral of the story is that Deltas are dynamic. Not only do they change as the underlying stock moves up and down, but they also change as expiration approaches.
Regards,
Brian (OG)
Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options.
While Delta represents the consensus of the marketplace as to the theoretical price movement of the option relative to the underlying security there is no guarantee that this forecast will be correct.
